the quotient of the number 3 and the difference between x and 2

The expression "the quotient of the number 3 and the difference between \( x \) and 2" can be translated into a mathematical expression.

1. **Quotient** generally refers to division.
2. **Difference between \( x \) and 2** means \( x - 2 \).

So, the mathematical expression for this statement would be:

\[
\frac{3}{x - 2}
\]

This represents the division of the number 3 by the difference between \( x \) and 2.

### Do you have any questions or would you like more details?

### Related Questions:
1. What happens if \( x = 2 \) in the expression \( \frac{3}{x - 2} \)?
2. How do we find the value of \( \frac{3}{x - 2} \) if \( x = 5 \)?
3. Can this expression be simplified further?
4. What is the domain of the function \( f(x) = \frac{3}{x - 2} \)?
5. How do we plot the graph of \( y = \frac{3}{x - 2} \)?

### Tip:
Remember, division by zero is undefined, so always check for values that make the denominator zero when working with fractions or rational expressions.

Explore the mathematical expression 'the quotient of the number 3 and the difference between x and 2'. Learn how to formulate and interpret \( \frac{3}{x - 2} \), a rational expression. Suitable for Grades 9-12.

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